Evidence from a large clinical trial shows that tamoxifen helps to reduce the incidence of breast cancer in women who are at increased risk for developing the disease. The U.S. Food and Drug Administration (FDA) has approved tamoxifen for such use. Raloxifene has been approved by the FDA for the prevention of osteoporosis (thinning of the bones) in postmenopausal women (women who have stopped menstruating). Researchers think that raloxifene may also reduce the risk of developing breast cancer and have fewer side effects than tamoxifen. The FDA consider the use of raloxifen for reducing the risk of breast cancer to be experimental at this time. This research study is being done to find out several things: - is raloxifene, also known by the trade name Evista, effective in reducing the occurence of breast cancer in women who are at increased risk for developing breast cancer? - if it is effective, how does raloxifene compare to tamoxifen, also known as Nolvadex, in reducing the incidence of breast cancer? - how do the side effects (good and bad) of raloxifene and tamoxifen compare? Up to 22,000 postmenopausal women will take part in this study in over 400 centers nationwide. 250 will be enrolled at this site.